Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×#322 | C2 | semidirect |
| 3. #69792 | C2 | semidirect |
| 4. #69738 | C2 | semidirect |
| 5. #69738 | C2 | semidirect |
| 34. C2×#322 | D3 | semidirect |
| 311. C3 | #9858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78463 | 2 |
| C2×C3×#322 | 2 |
| #69792 | 2 |
| #69738 | 2 |
| #69735 | 2 |
| #9858 | 3 |